### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

### Negative Dice

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

# Connect Three

##### Age 11 to 16Challenge Level

This game follows on from First Connect Three

The game Connect Three is played with two spinners, one with the numbers $1, 2, 3, -4, -5, -6$ and the other with the numbers $-1, -2, -3, 4, 5, 6$.

Spin the two spinners, choose what order to place the numbers in, and add or subtract them to produce one of the totals shown on the board, which you can then cover with one of your counters.

Can you place three of your counters in a straight line before your opponent does?

Play the game a few times, and then take a look at the questions below.
You can use the interactive version or print this board to play away from the computer.
Click on the purple cog to change the settings - you can play against a friend, or against three different levels of computer opponent.

Some numbers can only be made in one way, but some can be made in many different ways.

Can you work out the number of different ways of achieving each of the different totals?

Does this influence the way in which you might choose to play the game?

You may be interested in the other problems in our Explore and Explain Feature.